Simplify square root of 48n^3+ square root of 9n- square root of 3n

$\sqrt{48 n^{3}} + \sqrt{9 n} - \sqrt{3 n}$

Rewrite $48 n^{3}$ as ${(4 n)}^{2} \cdot (3 n)$ .

Factor $16$ out of $48$ .

$\sqrt{16 (3) n^{3}} + \sqrt{9 n} - \sqrt{3 n}$

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} \cdot 3 n^{3}} + \sqrt{9 n} - \sqrt{3 n}$

Factor out $n^{2}$ .

$\sqrt{4^{2} \cdot 3 (n^{2} n)} + \sqrt{9 n} - \sqrt{3 n}$

Move $3$ .

$\sqrt{4^{2} n^{2} \cdot 3 n} + \sqrt{9 n} - \sqrt{3 n}$

Rewrite $4^{2} n^{2}$ as ${(4 n)}^{2}$ .

$\sqrt{{(4 n)}^{2} \cdot 3 n} + \sqrt{9 n} - \sqrt{3 n}$

Add parentheses.

$\sqrt{{(4 n)}^{2} \cdot (3 n)} + \sqrt{9 n} - \sqrt{3 n}$

Pull terms out from under the radical.

$4 n \sqrt{3 n} + \sqrt{9 n} - \sqrt{3 n}$

Rewrite $9$ as $3^{2}$ .

$4 n \sqrt{3 n} + \sqrt{3^{2} n} - \sqrt{3 n}$

Pull terms out from under the radical.

$4 n \sqrt{3 n} + 3 \sqrt{n} - \sqrt{3 n}$